Subgroups — C₅₃×#60557 #27268069

Order 13568.

2038 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3126	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3125	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3124	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3123	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3122	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3121	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3120	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3119	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3091	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3076	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3035	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3002	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2943	C₂	1	2	yes	maximal, complemented
18	C₄×#135×C₅₃	C₂	1	2	yes	maximal, complemented
19	C₂×C₅₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×#135×C₅₃	C₂²	1	2	yes	—
22	C₂×#135×C₅₃	C₂²	1	2	yes	—
23	C₅₃×#542	C₂²	1	2	yes	—
24	C₅₃×#542	C₂²	1	2	yes	complemented
25	C₅₃×#541	C₂²	1	1	yes	characteristic
26	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
27	C₅₃×#540	C₂²	1	1	yes	characteristic
28	C₅₃×#540	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#539	—	2	2	no	—
30	C₅₃×#538	—	2	2	no	—
31	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#529	—	2	2	no	—
34	C₅₃×#529	—	2	2	no	—
35	C₅₃×#525	C₂²	1	2	yes	—
36	C₅₃×#520	—	2	2	no	—
37	C₅₃×#520	C₂²	1	2	yes	—
38	C₅₃×#520	C₂²	1	2	yes	—
39	C₅₃×#519	C₂²	1	1	yes	characteristic
40	C₅₃×#519	C₂²	1	1	yes	characteristic
41	C₅₃×#518	—	2	2	no	—
42	C₅₃×#518	C₂²	1	1	yes	characteristic
43	C₅₃×#518	C₂²	1	1	yes	characteristic
44	C₄×#41×C₅₃	—	2	2	no	—
45	C₄×#41×C₅₃	C₂²	1	2	yes	—
46	C₄×#41×C₅₃	C₂²	1	2	yes	—
47	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
48	C₂×#117×C₅₃	—	2	2	no	—
49	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#485	C₂²	1	2	yes	—
52	C₅₃×#485	C₂²	1	2	yes	—
53	C₅₃×#484	C₂²	1	2	yes	complemented
54	C₅₃×#483	C₂²	1	2	yes	complemented
55	C₅₃×#482	C₂²	1	2	yes	—
56	C₅₃×#482	C₂²	1	2	yes	—
57	C₅₃×#481	C₂²	1	2	yes	complemented
58	C₅₃×#480	C₂²	1	2	yes	complemented
59	C₅₃×#479	C₂²	1	2	yes	complemented
60	C₅₃×#479	C₂²	1	2	yes	complemented
61	C₅₃×#478	C₂²	1	2	yes	complemented
62	C₅₃×#478	C₂²	1	2	yes	complemented
63	C₅₃×#477	C₂²	1	2	yes	complemented
64	C₅₃×#476	C₂²	1	2	yes	complemented
65	C₅₃×#475	C₂²	1	2	yes	complemented
66	C₅₃×#474	C₂²	1	2	yes	complemented
67	C₅₃×#464	C₂²	1	2	yes	complemented
68	C₅₃×#464	C₂²	1	2	yes	complemented
69	C₅₃×#463	C₂²	1	2	yes	complemented
70	C₅₃×#463	C₂²	1	2	yes	complemented
71	C₅₃×#462	C₂²	1	2	yes	complemented
72	C₅₃×#461	C₂²	1	2	yes	complemented
73	C₅₃×#460	C₂²	1	2	yes	complemented
74	C₅₃×#459	C₂²	1	2	yes	complemented
75	C₅₃×#452	C₂²	1	2	yes	—
76	C₅₃×#452	C₂²	1	2	yes	—
77	C₅₃×#451	C₂²	1	2	yes	—
78	C₅₃×#450	C₂²	1	2	yes	—
79	C₅₃×#449	C₂²	1	2	yes	—
80	C₅₃×#449	C₂²	1	2	yes	—
81	C₅₃×#448	C₂²	1	2	yes	—
82	C₅₃×#447	C₂²	1	2	yes	—
83	C₅₃×#442	C₂²	1	2	yes	complemented
84	C₅₃×#442	C₂²	1	2	yes	complemented
85	C₅₃×#441	C₂²	1	2	yes	complemented
86	C₅₃×#441	C₂²	1	2	yes	complemented
87	C₅₃×#440	C₂²	1	2	yes	complemented
88	C₅₃×#440	C₂²	1	2	yes	complemented
89	C₅₃×#440	C₂²	1	2	yes	complemented
90	C₅₃×#440	C₂²	1	2	yes	complemented
91	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
92	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
93	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
94	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
95	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
96	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
97	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
98	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
99	C₅₃×#433	C₂²	1	2	yes	—
100	C₅₃×#433	C₂²	1	1	yes	characteristic
101	C₅₃×#433	C₂²	1	1	yes	characteristic
102	C₅₃×#433	C₂²	1	2	yes	complemented
103	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#427	C₂²	1	2	yes	complemented
106	C₅₃×#427	C₂²	1	2	yes	complemented
107	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
108	C₅₃×#416	C₂²	1	2	yes	—
109	C₅₃×#416	C₂²	1	2	yes	—
110	C₅₃×#416	C₂²	1	2	yes	complemented
111	C₅₃×#416	C₂²	1	2	yes	complemented
112	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
113	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₅₃	—	2	8	no	—
116	C₂×#41×C₅₃	—	2	1	no	—
117	C₂×#41×C₅₃	—	2	1	no	—
118	C₂×#41×C₅₃	C₂³	1	2	yes	—
119	C₂×#41×C₅₃	C₂³	1	2	yes	—
120	C₂×#41×C₅₃	C₂³	1	2	yes	—
121	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₅₃	—	2	1	no	—
123	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₅₃	—	2	1	no	—
125	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
126	#135×C₅₃	—	2	8	no	—
127	#135×C₅₃	—	2	8	no	—
128	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
129	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
133	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
134	C₂×D₈×C₅₃	C₂³	1	2	yes	—
135	C₂×D₈×C₅₃	C₂³	1	2	yes	—
136	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
137	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
140	#127×C₅₃	C₂³	1	1	yes	characteristic
141	#126×C₅₃	—	2	2	no	—
142	#126×C₅₃	—	2	2	no	—
143	#126×C₅₃	—	2	2	no	—
144	#126×C₅₃	—	2	2	no	—
145	#125×C₅₃	—	2	2	no	—
146	#125×C₅₃	—	2	2	no	—
147	#125×C₅₃	C₂³	1	1	yes	characteristic
148	#125×C₅₃	C₂³	1	1	yes	characteristic
149	#124×C₅₃	—	2	2	no	—
150	#124×C₅₃	—	2	2	no	—
151	#124×C₅₃	C₂³	1	2	yes	—
152	#123×C₅₃	—	2	2	no	—
153	#123×C₅₃	—	2	2	no	—
154	#123×C₅₃	—	2	2	no	—
155	#123×C₅₃	—	2	2	no	—
156	#123×C₅₃	—	2	2	no	—
157	C₂²⋊Q₈×C₅₃	—	2	2	no	—
158	C₂²⋊Q₈×C₅₃	—	2	2	no	—
159	C₂²⋊Q₈×C₅₃	—	2	2	no	—
160	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
161	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
162	#121×C₅₃	—	2	2	no	—
163	#121×C₅₃	—	2	2	no	—
164	#121×C₅₃	—	2	2	no	—
165	#121×C₅₃	C₂³	1	2	yes	—
166	#121×C₅₃	C₂³	1	2	yes	—
167	#120×C₅₃	—	2	2	no	—
168	C₄×Q₈×C₅₃	—	2	2	no	—
169	C₄×Q₈×C₅₃	—	2	2	no	—
170	C₄×Q₈×C₅₃	—	2	2	no	—
171	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
174	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
175	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
176	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
177	C₄×D₄×C₅₃	—	2	2	no	—
178	C₄×D₄×C₅₃	—	2	2	no	—
179	C₄×D₄×C₅₃	—	2	2	no	—
180	C₄×D₄×C₅₃	—	2	2	no	—
181	C₄×D₄×C₅₃	—	2	2	no	—
182	C₄×D₄×C₅₃	—	2	2	no	—
183	C₄×D₄×C₅₃	—	2	2	no	—
184	C₄×D₄×C₅₃	—	2	2	no	—
185	C₄×D₄×C₅₃	—	2	2	no	—
186	C₄×D₄×C₅₃	—	2	2	no	—
187	C₄×D₄×C₅₃	—	2	2	no	—
188	C₄×D₄×C₅₃	—	2	2	no	—
189	C₄×D₄×C₅₃	—	2	2	no	—
190	C₄×D₄×C₅₃	—	2	2	no	—
191	C₄×D₄×C₅₃	—	2	2	no	—
192	C₄×D₄×C₅₃	C₂³	1	2	yes	—
193	C₄×D₄×C₅₃	C₂³	1	2	yes	—
194	C₄×D₄×C₅₃	C₂³	1	2	yes	—
195	C₄×D₄×C₅₃	C₂³	1	2	yes	—
196	C₄×D₄×C₅₃	C₂³	1	2	yes	—
197	C₄×D₄×C₅₃	C₂³	1	2	yes	—
198	#117×C₅₃	—	2	2	no	—
199	#117×C₅₃	—	2	2	no	—
200	#117×C₅₃	—	2	2	no	—
201	#117×C₅₃	—	2	2	no	—
202	#117×C₅₃	—	2	2	no	—
203	#117×C₅₃	—	2	2	no	—
204	#117×C₅₃	—	2	2	no	—
205	#117×C₅₃	—	2	1	no	—
206	#117×C₅₃	—	2	1	no	—
207	#117×C₅₃	D₄	1	2	yes	—
208	#117×C₅₃	D₄	1	2	yes	—
209	#117×C₅₃	C₂³	1	1	yes	characteristic
210	#117×C₅₃	C₂³	1	1	yes	characteristic
211	#117×C₅₃	C₂³	1	2	yes	—
212	#117×C₅₃	C₂³	1	2	yes	—
213	#117×C₅₃	C₂³	1	1	yes	characteristic
214	#117×C₅₃	C₂³	1	1	yes	characteristic
215	#117×C₅₃	C₂³	1	1	yes	characteristic
216	#117×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
218	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
219	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
220	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
222	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
223	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
224	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
225	C₂×C₄²×C₅₃	—	2	2	no	—
226	C₂×C₄²×C₅₃	—	2	2	no	—
227	C₂×C₄²×C₅₃	—	2	2	no	—
228	C₂×C₄²×C₅₃	—	2	1	no	—
229	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
231	#107×C₅₃	C₂³	1	2	yes	—
232	#107×C₅₃	C₂³	1	2	yes	—
233	#107×C₅₃	C₂³	1	2	yes	—
234	#107×C₅₃	C₂³	1	2	yes	—
235	#106×C₅₃	C₂³	1	2	yes	—
236	#106×C₅₃	C₂³	1	2	yes	—
237	#106×C₅₃	C₂³	1	2	yes	—
238	#106×C₅₃	C₂³	1	2	yes	—
239	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
240	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
241	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
242	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
243	#103×C₅₃	C₂³	1	2	yes	—
244	#103×C₅₃	C₂³	1	2	yes	—
245	#103×C₅₃	C₂³	1	2	yes	—
246	#103×C₅₃	C₂³	1	2	yes	—
247	#103×C₅₃	C₂³	1	2	yes	—
248	#103×C₅₃	C₂³	1	2	yes	—
249	#103×C₅₃	C₂³	1	2	yes	—
250	#103×C₅₃	C₂³	1	2	yes	—
251	#102×C₅₃	C₂³	1	2	yes	—
252	#102×C₅₃	C₂³	1	2	yes	—
253	#102×C₅₃	C₂³	1	2	yes	—
254	#102×C₅₃	C₂³	1	2	yes	—
255	#102×C₅₃	C₂³	1	2	yes	—
256	#102×C₅₃	C₂³	1	2	yes	—
257	#102×C₅₃	C₂³	1	2	yes	—
258	#102×C₅₃	C₂³	1	2	yes	—
259	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
260	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
261	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
262	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
263	#97×C₅₃	C₂³	1	1	yes	characteristic
264	#97×C₅₃	C₂³	1	2	yes	—
265	#97×C₅₃	C₂³	1	1	yes	characteristic
266	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
267	C₄×C₈×C₅₃	C₂³	1	2	yes	—
268	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
269	C₂⁴×C₅₃	—	2	1	no	—
270	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
271	#41×C₅₃	—	2	8	no	—
272	#41×C₅₃	—	2	8	no	—
273	#41×C₅₃	—	2	4	no	—
274	#41×C₅₃	—	2	4	no	—
275	#41×C₅₃	—	2	4	no	—
276	#41×C₅₃	—	2	4	no	—
277	#41×C₅₃	—	2	4	no	—
278	#41×C₅₃	#41	1	8	yes	—
279	C₂×Q₈×C₅₃	—	2	4	no	—
280	C₂×Q₈×C₅₃	—	2	1	no	—
281	C₂×Q₈×C₅₃	—	2	2	no	—
282	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
283	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
284	C₂×D₄×C₅₃	—	2	8	no	—
285	C₂×D₄×C₅₃	—	2	2	no	—
286	C₂×D₄×C₅₃	—	2	2	no	—
287	C₂×D₄×C₅₃	—	2	4	no	—
288	C₂×D₄×C₅₃	—	2	2	no	—
289	C₂×D₄×C₅₃	—	2	2	no	—
290	C₂×D₄×C₅₃	—	2	2	no	—
291	C₂×D₄×C₅₃	—	2	1	no	—
292	C₂×D₄×C₅₃	—	2	2	no	—
293	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
294	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₅₃	—	2	8	no	—
296	C₂²×C₄×C₅₃	—	2	1	no	—
297	C₂²×C₄×C₅₃	—	2	2	no	—
298	C₂²×C₄×C₅₃	—	2	2	no	—
299	C₂²×C₄×C₅₃	—	2	4	no	—
300	C₂²×C₄×C₅₃	—	2	2	no	—
301	C₂²×C₄×C₅₃	—	2	2	no	—
302	C₂²×C₄×C₅₃	—	2	2	no	—
303	C₂²×C₄×C₅₃	—	2	2	no	—
304	C₂²×C₄×C₅₃	—	2	2	no	—
305	C₂²×C₄×C₅₃	—	2	2	no	—
306	C₂²×C₄×C₅₃	—	2	2	no	—
307	C₂²×C₄×C₅₃	—	2	2	no	—
308	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
312	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
313	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
316	Q₁₆×C₅₃	—	2	4	no	—
317	Q₁₆×C₅₃	—	2	4	no	—
318	SD₁₆×C₅₃	—	2	4	no	—
319	SD₁₆×C₅₃	—	2	4	no	—
320	SD₁₆×C₅₃	—	2	4	no	—
321	SD₁₆×C₅₃	—	2	4	no	—
322	D₈×C₅₃	—	2	4	no	—
323	D₈×C₅₃	—	2	4	no	—
324	C₂×C₈×C₅₃	—	2	4	no	—
325	C₂×C₈×C₅₃	—	2	4	no	—
326	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
327	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
328	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
329	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
330	C₄⋊C₄×C₅₃	—	2	2	no	—
331	C₄⋊C₄×C₅₃	—	2	2	no	—
332	C₄⋊C₄×C₅₃	—	2	2	no	—
333	C₄⋊C₄×C₅₃	—	2	2	no	—
334	C₄⋊C₄×C₅₃	—	2	2	no	—
335	C₄⋊C₄×C₅₃	—	2	2	no	—
336	C₄⋊C₄×C₅₃	—	2	2	no	—
337	C₄⋊C₄×C₅₃	—	2	2	no	—
338	C₄⋊C₄×C₅₃	—	2	2	no	—
339	C₄⋊C₄×C₅₃	—	2	2	no	—
340	C₄⋊C₄×C₅₃	—	2	2	no	—
341	C₄⋊C₄×C₅₃	—	2	2	no	—
342	C₄⋊C₄×C₅₃	—	2	2	no	—
343	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
344	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
345	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
346	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
347	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
349	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
350	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
351	C₂²⋊C₄×C₅₃	—	2	1	no	—
352	C₂²⋊C₄×C₅₃	—	2	1	no	—
353	C₂²⋊C₄×C₅₃	—	2	2	no	—
354	C₂²⋊C₄×C₅₃	—	2	2	no	—
355	C₂²⋊C₄×C₅₃	—	2	2	no	—
356	C₂²⋊C₄×C₅₃	—	2	2	no	—
357	C₂²⋊C₄×C₅₃	—	2	2	no	—
358	C₂²⋊C₄×C₅₃	—	2	2	no	—
359	C₂²⋊C₄×C₅₃	—	2	2	no	—
360	C₂²⋊C₄×C₅₃	—	2	2	no	—
361	C₂²⋊C₄×C₅₃	—	2	2	no	—
362	C₂²⋊C₄×C₅₃	—	2	2	no	—
363	C₂²⋊C₄×C₅₃	—	2	2	no	—
364	C₂²⋊C₄×C₅₃	—	2	2	no	—
365	C₂²⋊C₄×C₅₃	—	2	2	no	—
366	C₂²⋊C₄×C₅₃	—	2	2	no	—
367	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
368	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
369	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
370	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
371	C₄²×C₅₃	—	2	2	no	—
372	C₄²×C₅₃	—	2	2	no	—
373	C₄²×C₅₃	—	2	2	no	—
374	C₄²×C₅₃	—	2	2	no	—
375	C₄²×C₅₃	—	2	1	no	—
376	C₄²×C₅₃	—	2	1	no	—
377	C₄²×C₅₃	—	2	2	no	—
378	C₄²×C₅₃	—	2	2	no	—
379	C₄²×C₅₃	—	2	2	no	—
380	C₄²×C₅₃	—	2	2	no	—
381	C₄²×C₅₃	C₂×D₄	1	2	yes	—
382	C₄²×C₅₃	C₂×D₄	1	2	yes	—
383	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂³×C₅₃	—	2	4	no	—
388	C₂³×C₅₃	—	2	2	no	—
389	C₂³×C₅₃	—	2	2	no	—
390	C₂³×C₅₃	—	2	2	no	—
391	C₂³×C₅₃	—	4	2	no	—
392	C₂³×C₅₃	—	8	2	no	—
393	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
394	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
395	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
396	Q₈×C₅₃	—	2	4	no	—
397	Q₈×C₅₃	—	2	2	no	—
398	Q₈×C₅₃	—	2	2	no	—
399	Q₈×C₅₃	—	2	2	no	—
400	Q₈×C₅₃	—	8	2	no	—
401	Q₈×C₅₃	C₂×#41	1	4	yes	—
402	D₄×C₅₃	—	2	8	no	—
403	D₄×C₅₃	—	2	4	no	—
404	D₄×C₅₃	—	2	8	no	—
405	D₄×C₅₃	—	2	2	no	—
406	D₄×C₅₃	—	2	2	no	—
407	D₄×C₅₃	—	2	2	no	—
408	D₄×C₅₃	—	4	4	no	—
409	D₄×C₅₃	—	8	2	no	—
410	D₄×C₅₃	—	8	2	no	—
411	D₄×C₅₃	—	8	2	no	—
412	D₄×C₅₃	C₂×#41	1	4	yes	—
413	C₂×C₄×C₅₃	—	2	4	no	—
414	C₂×C₄×C₅₃	—	2	8	no	—
415	C₂×C₄×C₅₃	—	2	2	no	—
416	C₂×C₄×C₅₃	—	2	2	no	—
417	C₂×C₄×C₅₃	—	2	2	no	—
418	C₂×C₄×C₅₃	—	2	8	no	—
419	C₂×C₄×C₅₃	—	2	2	no	—
420	C₂×C₄×C₅₃	—	2	2	no	—
421	C₂×C₄×C₅₃	—	2	2	no	—
422	C₂×C₄×C₅₃	—	2	2	no	—
423	C₂×C₄×C₅₃	—	2	2	no	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	2	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	4	2	no	—
428	C₂×C₄×C₅₃	—	4	2	no	—
429	C₂×C₄×C₅₃	—	4	4	no	—
430	C₂×C₄×C₅₃	—	8	2	no	—
431	C₂×C₄×C₅₃	—	8	2	no	—
432	C₂×C₄×C₅₃	—	8	2	no	—
433	C₂×C₄×C₅₃	—	8	2	no	—
434	C₂×C₄×C₅₃	—	8	2	no	—
435	C₂×C₄×C₅₃	—	8	2	no	—
436	C₂×C₄×C₅₃	—	8	2	no	—
437	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
442	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
445	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
446	C₈×C₅₃	—	2	2	no	—
447	C₈×C₅₃	—	2	2	no	—
448	C₈×C₅₃	—	2	2	no	—
449	C₈×C₅₃	—	2	2	no	—
450	#60557	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂²×C₅₃	—	2	2	no	—
452	C₂²×C₅₃	—	2	2	no	—
453	C₂²×C₅₃	—	2	2	no	—
454	C₂²×C₅₃	—	2	1	no	—
455	C₂²×C₅₃	—	2	1	no	—
456	C₂²×C₅₃	—	2	4	no	—
457	C₂²×C₅₃	—	4	2	no	—
458	C₂²×C₅₃	—	4	2	no	—
459	C₂²×C₅₃	—	4	2	no	—
460	C₂²×C₅₃	—	4	2	no	—
461	C₂²×C₅₃	—	4	2	no	—
462	C₂²×C₅₃	—	8	2	no	—
463	C₂²×C₅₃	—	8	4	no	—
464	C₂²×C₅₃	#525	1	2	yes	—
465	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
466	C₄×C₅₃	—	2	2	no	—
467	C₄×C₅₃	—	2	2	no	—
468	C₄×C₅₃	—	2	2	no	—
469	C₄×C₅₃	—	2	2	no	—
470	C₄×C₅₃	—	2	1	no	—
471	C₄×C₅₃	—	2	4	no	—
472	C₄×C₅₃	—	2	1	no	—
473	C₄×C₅₃	—	4	2	no	—
474	C₄×C₅₃	—	4	2	no	—
475	C₄×C₅₃	—	4	2	no	—
476	C₄×C₅₃	—	4	2	no	—
477	C₄×C₅₃	—	4	2	no	—
478	C₄×C₅₃	#525	1	2	yes	—
479	C₄×C₅₃	C₂²×#41	1	2	yes	—
480	#3455	C₂×C₅₃	1	1	yes	characteristic, complemented
481	#3428	C₂×C₅₃	1	1	yes	characteristic, complemented
482	#3127	C₂×C₅₃	1	1	yes	characteristic, complemented
483	#3126	C₂×C₅₃	1	1	yes	characteristic, complemented
484	#3125	C₂×C₅₃	1	2	yes	complemented
485	#3124	C₂×C₅₃	1	2	yes	complemented
486	#3123	C₂×C₅₃	1	1	yes	characteristic, complemented
487	#3122	C₂×C₅₃	1	1	yes	characteristic, complemented
488	#3121	C₂×C₅₃	1	2	yes	complemented
489	#3120	C₂×C₅₃	1	2	yes	complemented
490	#3119	C₂×C₅₃	1	2	yes	complemented
491	#3118	C₂×C₅₃	1	2	yes	complemented
492	#3091	C₂×C₅₃	1	2	yes	complemented
493	#3076	C₂×C₅₃	1	2	yes	complemented
494	#3035	C₂×C₅₃	1	2	yes	complemented
495	#3002	C₂×C₅₃	1	2	yes	complemented
496	#2943	C₂×C₅₃	1	2	yes	complemented
497	C₄×#135	C₂×C₅₃	1	2	yes	complemented
498	C₂×#433	C₂×C₅₃	1	1	yes	characteristic, complemented
499	C₂×C₅₃	—	2	2	no	—
500	C₂×C₅₃	—	4	1	no	—
501	C₂×C₅₃	—	4	1	no	—
502	C₂×C₅₃	—	4	4	no	—
503	C₂×C₅₃	—	8	2	no	—
504	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
505	C₂×C₅₃	#3584	1	2	yes	—
506	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
507	C₂×#135	C₂²×C₅₃	1	2	yes	—
508	C₂×#135	C₂²×C₅₃	1	2	yes	—
509	#542	C₂²×C₅₃	1	2	yes	—
510	#542	C₂²×C₅₃	1	2	yes	complemented
511	#541	C₂²×C₅₃	1	1	yes	characteristic
512	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
513	#540	C₂²×C₅₃	1	1	yes	characteristic
514	#540	C₂²×C₅₃	1	1	yes	characteristic, complemented
515	#539	—	2	2	no	—
516	#538	—	2	2	no	—
517	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
518	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
519	#529	—	2	2	no	—
520	#529	—	2	2	no	—
521	#525	C₂²×C₅₃	1	2	yes	—
522	#520	—	2	2	no	—
523	#520	C₂²×C₅₃	1	2	yes	—
524	#520	C₂²×C₅₃	1	2	yes	—
525	#519	C₂²×C₅₃	1	1	yes	characteristic
526	#519	C₂²×C₅₃	1	1	yes	characteristic
527	#518	—	2	2	no	—
528	#518	C₂²×C₅₃	1	1	yes	characteristic
529	#518	C₂²×C₅₃	1	1	yes	characteristic
530	C₄×#41	—	2	2	no	—
531	C₄×#41	C₂²×C₅₃	1	2	yes	—
532	C₄×#41	C₂²×C₅₃	1	2	yes	—
533	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
534	C₂×#117	—	2	2	no	—
535	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
536	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
537	#485	C₂²×C₅₃	1	2	yes	—
538	#485	C₂²×C₅₃	1	2	yes	—
539	#484	C₂²×C₅₃	1	2	yes	complemented
540	#483	C₂²×C₅₃	1	2	yes	complemented
541	#482	C₂²×C₅₃	1	2	yes	—
542	#482	C₂²×C₅₃	1	2	yes	—
543	#481	C₂²×C₅₃	1	2	yes	complemented
544	#480	C₂²×C₅₃	1	2	yes	complemented
545	#479	C₂²×C₅₃	1	2	yes	complemented
546	#479	C₂²×C₅₃	1	2	yes	complemented
547	#478	C₂²×C₅₃	1	2	yes	complemented
548	#478	C₂²×C₅₃	1	2	yes	complemented
549	#477	C₂²×C₅₃	1	2	yes	complemented
550	#476	C₂²×C₅₃	1	2	yes	complemented
551	#475	C₂²×C₅₃	1	2	yes	complemented
552	#474	C₂²×C₅₃	1	2	yes	complemented
553	#464	C₂²×C₅₃	1	2	yes	complemented
554	#464	C₂²×C₅₃	1	2	yes	complemented
555	#463	C₂²×C₅₃	1	2	yes	complemented
556	#463	C₂²×C₅₃	1	2	yes	complemented
557	#462	C₂²×C₅₃	1	2	yes	complemented
558	#461	C₂²×C₅₃	1	2	yes	complemented
559	#460	C₂²×C₅₃	1	2	yes	complemented
560	#459	C₂²×C₅₃	1	2	yes	complemented
561	#452	C₂²×C₅₃	1	2	yes	—
562	#452	C₂²×C₅₃	1	2	yes	—
563	#451	C₂²×C₅₃	1	2	yes	—
564	#450	C₂²×C₅₃	1	2	yes	—
565	#449	C₂²×C₅₃	1	2	yes	—
566	#449	C₂²×C₅₃	1	2	yes	—
567	#448	C₂²×C₅₃	1	2	yes	—
568	#447	C₂²×C₅₃	1	2	yes	—
569	#442	C₂²×C₅₃	1	2	yes	complemented
570	#442	C₂²×C₅₃	1	2	yes	complemented
571	#441	C₂²×C₅₃	1	2	yes	complemented
572	#441	C₂²×C₅₃	1	2	yes	complemented
573	#440	C₂²×C₅₃	1	2	yes	complemented
574	#440	C₂²×C₅₃	1	2	yes	complemented
575	#440	C₂²×C₅₃	1	2	yes	complemented
576	#440	C₂²×C₅₃	1	2	yes	complemented
577	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
578	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
579	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
580	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
581	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
582	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
583	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
584	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
585	#433	C₂²×C₅₃	1	2	yes	—
586	#433	C₂²×C₅₃	1	1	yes	characteristic
587	#433	C₂²×C₅₃	1	1	yes	characteristic
588	#433	C₂²×C₅₃	1	2	yes	complemented
589	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
590	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
591	#427	C₂²×C₅₃	1	2	yes	complemented
592	#427	C₂²×C₅₃	1	2	yes	complemented
593	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
594	#416	C₂²×C₅₃	1	2	yes	—
595	#416	C₂²×C₅₃	1	2	yes	—
596	#416	C₂²×C₅₃	1	2	yes	complemented
597	#416	C₂²×C₅₃	1	2	yes	complemented
598	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
599	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
600	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
601	C₅₃	#60557	1	1	yes	characteristic, direct product factor, Sylow
602	C₂×#41	—	2	8	no	—
603	C₂×#41	—	2	1	no	—
604	C₂×#41	—	2	1	no	—
605	C₂×#41	C₂³×C₅₃	1	2	yes	—
606	C₂×#41	C₂³×C₅₃	1	2	yes	—
607	C₂×#41	C₂³×C₅₃	1	2	yes	—
608	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
609	C₂²×D₄	—	2	1	no	—
610	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
611	C₂³×C₄	—	2	1	no	—
612	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
613	#135	—	2	8	no	—
614	#135	—	2	8	no	—
615	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
616	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
617	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
618	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
619	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
620	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
621	C₂×D₈	C₂³×C₅₃	1	2	yes	—
622	C₂×D₈	C₂³×C₅₃	1	2	yes	—
623	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
624	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
625	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
626	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
627	#127	C₂³×C₅₃	1	1	yes	characteristic
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#125	—	2	2	no	—
633	#125	—	2	2	no	—
634	#125	C₂³×C₅₃	1	1	yes	characteristic
635	#125	C₂³×C₅₃	1	1	yes	characteristic
636	#124	—	2	2	no	—
637	#124	—	2	2	no	—
638	#124	C₂³×C₅₃	1	2	yes	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	—	2	2	no	—
643	#123	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
648	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	C₂³×C₅₃	1	2	yes	—
653	#121	C₂³×C₅₃	1	2	yes	—
654	#120	—	2	2	no	—
655	C₄×Q₈	—	2	2	no	—
656	C₄×Q₈	—	2	2	no	—
657	C₄×Q₈	—	2	2	no	—
658	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
659	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
660	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
661	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
662	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
663	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	C₂³×C₅₃	1	2	yes	—
680	C₄×D₄	C₂³×C₅₃	1	2	yes	—
681	C₄×D₄	C₂³×C₅₃	1	2	yes	—
682	C₄×D₄	C₂³×C₅₃	1	2	yes	—
683	C₄×D₄	C₂³×C₅₃	1	2	yes	—
684	C₄×D₄	C₂³×C₅₃	1	2	yes	—
685	#117	—	2	1	no	—
686	#117	—	2	1	no	—
687	#117	—	2	2	no	—
688	#117	—	2	2	no	—
689	#117	—	2	2	no	—
690	#117	—	2	2	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	D₄×C₅₃	1	2	yes	—
695	#117	D₄×C₅₃	1	2	yes	—
696	#117	C₂³×C₅₃	1	2	yes	—
697	#117	C₂³×C₅₃	1	1	yes	characteristic
698	#117	C₂³×C₅₃	1	1	yes	characteristic
699	#117	C₂³×C₅₃	1	2	yes	—
700	#117	C₂³×C₅₃	1	1	yes	characteristic
701	#117	C₂³×C₅₃	1	1	yes	characteristic
702	#117	C₂³×C₅₃	1	1	yes	characteristic
703	#117	C₂³×C₅₃	1	1	yes	characteristic
704	C₂×C₄⋊C₄	—	2	2	no	—
705	C₂×C₄⋊C₄	—	2	2	no	—
706	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
708	C₂×C₂²⋊C₄	—	2	1	no	—
709	C₂×C₂²⋊C₄	—	2	2	no	—
710	C₂×C₂²⋊C₄	—	2	2	no	—
711	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
712	C₂×C₄²	—	2	1	no	—
713	C₂×C₄²	—	2	2	no	—
714	C₂×C₄²	—	2	2	no	—
715	C₂×C₄²	—	2	2	no	—
716	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
718	#107	C₂³×C₅₃	1	2	yes	—
719	#107	C₂³×C₅₃	1	2	yes	—
720	#107	C₂³×C₅₃	1	2	yes	—
721	#107	C₂³×C₅₃	1	2	yes	—
722	#106	C₂³×C₅₃	1	2	yes	—
723	#106	C₂³×C₅₃	1	2	yes	—
724	#106	C₂³×C₅₃	1	2	yes	—
725	#106	C₂³×C₅₃	1	2	yes	—
726	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
727	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
728	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
729	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
730	#103	C₂³×C₅₃	1	2	yes	—
731	#103	C₂³×C₅₃	1	2	yes	—
732	#103	C₂³×C₅₃	1	2	yes	—
733	#103	C₂³×C₅₃	1	2	yes	—
734	#103	C₂³×C₅₃	1	2	yes	—
735	#103	C₂³×C₅₃	1	2	yes	—
736	#103	C₂³×C₅₃	1	2	yes	—
737	#103	C₂³×C₅₃	1	2	yes	—
738	#102	C₂³×C₅₃	1	2	yes	—
739	#102	C₂³×C₅₃	1	2	yes	—
740	#102	C₂³×C₅₃	1	2	yes	—
741	#102	C₂³×C₅₃	1	2	yes	—
742	#102	C₂³×C₅₃	1	2	yes	—
743	#102	C₂³×C₅₃	1	2	yes	—
744	#102	C₂³×C₅₃	1	2	yes	—
745	#102	C₂³×C₅₃	1	2	yes	—
746	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
747	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
748	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
749	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
750	#97	C₂³×C₅₃	1	1	yes	characteristic
751	#97	C₂³×C₅₃	1	2	yes	—
752	#97	C₂³×C₅₃	1	1	yes	characteristic
753	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
754	C₄×C₈	C₂³×C₅₃	1	2	yes	—
755	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
756	C₂⁴	—	2	1	no	—
757	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
758	#41	—	2	8	no	—
759	#41	—	2	8	no	—
760	#41	—	2	4	no	—
761	#41	—	2	4	no	—
762	#41	—	2	4	no	—
763	#41	—	2	4	no	—
764	#41	—	2	4	no	—
765	#41	#41×C₅₃	1	8	yes	—
766	C₂×Q₈	—	2	4	no	—
767	C₂×Q₈	—	2	1	no	—
768	C₂×Q₈	—	2	2	no	—
769	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
770	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
771	C₂×D₄	—	2	8	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	1	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
781	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
782	C₂²×C₄	—	2	8	no	—
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	4	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
799	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
803	Q₁₆	—	2	4	no	—
804	Q₁₆	—	2	4	no	—
805	SD₁₆	—	2	4	no	—
806	SD₁₆	—	2	4	no	—
807	SD₁₆	—	2	4	no	—
808	SD₁₆	—	2	4	no	—
809	D₈	—	2	4	no	—
810	D₈	—	2	4	no	—
811	C₂×C₈	—	2	4	no	—
812	C₂×C₈	—	2	4	no	—
813	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
814	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
815	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
816	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
831	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
832	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
833	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
834	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
835	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
837	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
838	C₂²⋊C₄	—	2	1	no	—
839	C₂²⋊C₄	—	2	1	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
855	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
856	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
857	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
858	C₄²	—	2	2	no	—
859	C₄²	—	2	2	no	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	1	no	—
864	C₄²	—	2	1	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	C₂×D₄×C₅₃	1	2	yes	—
869	C₄²	C₂×D₄×C₅₃	1	2	yes	—
870	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
871	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
872	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
873	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
874	C₂³	—	2	4	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	4	2	no	—
879	C₂³	—	8	2	no	—
880	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
881	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
882	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
883	Q₈	—	2	4	no	—
884	Q₈	—	2	2	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	2	2	no	—
887	Q₈	—	8	2	no	—
888	Q₈	C₂×#41×C₅₃	1	4	yes	—
889	D₄	—	2	8	no	—
890	D₄	—	2	4	no	—
891	D₄	—	2	8	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	2	2	no	—
895	D₄	—	4	4	no	—
896	D₄	—	8	2	no	—
897	D₄	—	8	2	no	—
898	D₄	—	8	2	no	—
899	D₄	C₂×#41×C₅₃	1	4	yes	—
900	C₂×C₄	—	2	4	no	—
901	C₂×C₄	—	2	8	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	8	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	2	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	8	2	no	—
918	C₂×C₄	—	8	2	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	—	8	2	no	—
924	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
927	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
928	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
929	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
931	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
932	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
933	C₈	—	2	2	no	—
934	C₈	—	2	2	no	—
935	C₈	—	2	2	no	—
936	C₈	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	4	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	8	2	no	—
949	C₂²	—	8	4	no	—
950	C₂²	C₅₃×#525	1	2	yes	—
951	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	4	no	—
958	C₄	—	2	1	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	C₅₃×#525	1	2	yes	—
965	C₄	C₂²×#41×C₅₃	1	2	yes	—
966	C₂	—	2	2	no	—
967	C₂	—	4	1	no	—
968	C₂	—	4	1	no	—
969	C₂	—	4	4	no	—
970	C₂	—	8	2	no	—
971	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
972	C₂	C₅₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
socle	C₂²×C₅₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₂×#117×C₅₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₃×#3455	C₂	semidirect
2. C₅₃×#3428	C₂	semidirect
3. C₅₃×#3127	C₂	semidirect
4. C₅₃×#3126	C₂	semidirect
5. C₅₃×#3125	C₂	semidirect
6. C₅₃×#3124	C₂	semidirect
7. C₅₃×#3123	C₂	semidirect
8. C₅₃×#3122	C₂	semidirect
9. C₅₃×#3121	C₂	semidirect
10. C₅₃×#3120	C₂	semidirect
11. C₅₃×#3119	C₂	semidirect
12. C₅₃×#3118	C₂	semidirect
13. C₅₃×#3091	C₂	semidirect
14. C₅₃×#3076	C₂	semidirect
15. C₅₃×#3035	C₂	semidirect
16. C₅₃×#3002	C₂	semidirect
17. C₅₃×#2943	C₂	semidirect
18. C₄×#135×C₅₃	C₂	semidirect
19. C₂×C₅₃×#433	C₂	semidirect
24. C₅₃×#542	C₂²	semidirect
26. C₅₃×#541	C₂²	semidirect
28. C₅₃×#540	C₂²	semidirect
31. C₅₃×#533	C₂²	semidirect
32. C₅₃×#532	C₂²	semidirect
47. C₄×#41×C₅₃	C₂²	semidirect
53. C₅₃×#484	C₂²	semidirect
54. C₅₃×#483	C₂²	semidirect
57. C₅₃×#481	C₂²	semidirect
58. C₅₃×#480	C₂²	semidirect
59. C₅₃×#479	C₂²	semidirect
60. C₅₃×#479	C₂²	semidirect
61. C₅₃×#478	C₂²	semidirect
62. C₅₃×#478	C₂²	semidirect
63. C₅₃×#477	C₂²	semidirect
64. C₅₃×#476	C₂²	semidirect
65. C₅₃×#475	C₂²	semidirect
66. C₅₃×#474	C₂²	semidirect
67. C₅₃×#464	C₂²	semidirect
68. C₅₃×#464	C₂²	semidirect
69. C₅₃×#463	C₂²	semidirect
70. C₅₃×#463	C₂²	semidirect
71. C₅₃×#462	C₂²	semidirect
72. C₅₃×#461	C₂²	semidirect
73. C₅₃×#460	C₂²	semidirect
74. C₅₃×#459	C₂²	semidirect
83. C₅₃×#442	C₂²	semidirect
84. C₅₃×#442	C₂²	semidirect
85. C₅₃×#441	C₂²	semidirect
86. C₅₃×#441	C₂²	semidirect
87. C₅₃×#440	C₂²	semidirect
88. C₅₃×#440	C₂²	semidirect
89. C₅₃×#440	C₂²	semidirect
90. C₅₃×#440	C₂²	semidirect
91. C₄×Q₁₆×C₅₃	C₂²	semidirect
92. C₄×Q₁₆×C₅₃	C₂²	semidirect
93. C₄×SD₁₆×C₅₃	C₂²	semidirect
94. C₄×SD₁₆×C₅₃	C₂²	semidirect
95. C₄×SD₁₆×C₅₃	C₂²	semidirect
96. C₄×SD₁₆×C₅₃	C₂²	semidirect
97. C₄×D₈×C₅₃	C₂²	semidirect
98. C₄×D₈×C₅₃	C₂²	semidirect
102. C₅₃×#433	C₂²	semidirect
103. C₅₃×#433	C₂²	semidirect
104. C₅₃×#433	C₂²	semidirect
105. C₅₃×#427	C₂²	semidirect
106. C₅₃×#427	C₂²	semidirect
107. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
110. C₅₃×#416	C₂²	semidirect
111. C₅₃×#416	C₂²	semidirect
113. C₂×#97×C₅₃	C₂²	semidirect
114. C₂×C₄×C₈×C₅₃	C₂²	semidirect
450. #60557	C₅₃	direct (N × H)
480. #3455	C₂×C₅₃	semidirect
481. #3428	C₂×C₅₃	semidirect
482. #3127	C₂×C₅₃	semidirect
483. #3126	C₂×C₅₃	semidirect
484. #3125	C₂×C₅₃	semidirect
485. #3124	C₂×C₅₃	semidirect
486. #3123	C₂×C₅₃	semidirect
487. #3122	C₂×C₅₃	semidirect
488. #3121	C₂×C₅₃	semidirect
489. #3120	C₂×C₅₃	semidirect
490. #3119	C₂×C₅₃	semidirect
491. #3118	C₂×C₅₃	semidirect
492. #3091	C₂×C₅₃	semidirect
493. #3076	C₂×C₅₃	semidirect
494. #3035	C₂×C₅₃	semidirect
495. #3002	C₂×C₅₃	semidirect
496. #2943	C₂×C₅₃	semidirect
497. C₄×#135	C₂×C₅₃	semidirect
498. C₂×#433	C₂×C₅₃	semidirect
510. #542	C₂²×C₅₃	semidirect
512. #541	C₂²×C₅₃	semidirect
514. #540	C₂²×C₅₃	semidirect
517. #533	C₂²×C₅₃	semidirect
518. #532	C₂²×C₅₃	semidirect
533. C₄×#41	C₂²×C₅₃	semidirect
539. #484	C₂²×C₅₃	semidirect
540. #483	C₂²×C₅₃	semidirect
543. #481	C₂²×C₅₃	semidirect
544. #480	C₂²×C₅₃	semidirect
545. #479	C₂²×C₅₃	semidirect
546. #479	C₂²×C₅₃	semidirect
547. #478	C₂²×C₅₃	semidirect
548. #478	C₂²×C₅₃	semidirect
549. #477	C₂²×C₅₃	semidirect
550. #476	C₂²×C₅₃	semidirect
551. #475	C₂²×C₅₃	semidirect
552. #474	C₂²×C₅₃	semidirect
553. #464	C₂²×C₅₃	semidirect
554. #464	C₂²×C₅₃	semidirect
555. #463	C₂²×C₅₃	semidirect
556. #463	C₂²×C₅₃	semidirect
557. #462	C₂²×C₅₃	semidirect
558. #461	C₂²×C₅₃	semidirect
559. #460	C₂²×C₅₃	semidirect
560. #459	C₂²×C₅₃	semidirect
569. #442	C₂²×C₅₃	semidirect
570. #442	C₂²×C₅₃	semidirect
571. #441	C₂²×C₅₃	semidirect
572. #441	C₂²×C₅₃	semidirect
573. #440	C₂²×C₅₃	semidirect
574. #440	C₂²×C₅₃	semidirect
575. #440	C₂²×C₅₃	semidirect
576. #440	C₂²×C₅₃	semidirect
577. C₄×Q₁₆	C₂²×C₅₃	semidirect
578. C₄×Q₁₆	C₂²×C₅₃	semidirect
579. C₄×SD₁₆	C₂²×C₅₃	semidirect
580. C₄×SD₁₆	C₂²×C₅₃	semidirect
581. C₄×SD₁₆	C₂²×C₅₃	semidirect
582. C₄×SD₁₆	C₂²×C₅₃	semidirect
583. C₄×D₈	C₂²×C₅₃	semidirect
584. C₄×D₈	C₂²×C₅₃	semidirect
588. #433	C₂²×C₅₃	semidirect
589. #433	C₂²×C₅₃	semidirect
590. #433	C₂²×C₅₃	semidirect
591. #427	C₂²×C₅₃	semidirect
592. #427	C₂²×C₅₃	semidirect
593. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
596. #416	C₂²×C₅₃	semidirect
597. #416	C₂²×C₅₃	semidirect
599. C₂×#97	C₂²×C₅₃	semidirect
600. C₂×C₄×C₈	C₂²×C₅₃	semidirect
601. C₅₃	#60557	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3455	2
C₅₃×#3428	2
C₅₃×#3127	2
C₅₃×#3126	2
C₅₃×#3125	2
C₅₃×#3124	2
C₅₃×#3123	2
C₅₃×#3122	2
C₅₃×#3121	2
C₅₃×#3120	2
C₅₃×#3119	2
C₅₃×#3118	2
C₅₃×#3091	2
C₅₃×#3076	2
C₅₃×#3035	2
C₅₃×#3002	2
C₅₃×#2943	2
C₄×#135×C₅₃	2
C₂×C₅₃×#433	2
#60557	53

Subgroups — C53×#60557 #27268069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60557 #27268069